Have you checked/replaced all the electricals?  Like the spark plugs, dizzy
cap, rotor arm, points, condenser, HT leads etc?   Also what state is the
battery in?  Oh and top up the carb. dashpot with a little engine oil too.

I'd check these out first, then if the problem persists I'd get it crypton
tuned after that I'd seek out a good Mini specialist or if there's none in
your area (for instance if their hundreds of miles away, like in my case)
get it looked at by a good qualified gearbox specialist as maybe the
auto-box has had it's day.  Reconditioned replacements are available, but
they cost a bit.

All the best,

Taffy